Question

If tan² 45° − cos² 30° = x sin 45° cos 45°, then x = 

Options

• 2

•  −2

• \[- \frac{1}{2}\]

• \[\frac{1}{2}\]

Answer 1

We are given:` tan^2 45°-cos^2 30°=x sin 45° cos 45°`

We have to find x 

⇒` 1-(sqrt3/2)^2=x 1/sqrt2 xx1/sqrt2` 

⇒ `1-3/4=x/2` 

⇒ `1/4=x/2`

⇒`x=1/2` 

We know that  ` sin°45=1/sqrt2 , cos 45°=1/sqrt2, tan 45°=1, cos 30°=sqrt3/2`